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All content in this area was uploaded by Raphaël Nussbaumer on Jul 02, 2019

Content may be subject to copyright.

A geostatistical approach to estimate high resolution

nocturnal bird migration densities from a weather radar

network.

Rapha¨el Nussbaumer1,2,* , Lionel Benoit2, Gr´egoire Mariethoz2, Felix

Liechti1, Silke Bauer1& Baptiste Schmid1

1 Swiss Ornithological Institute, Sempach, Switzerland

2 Institute of Earth Surface Dynamics, University of Lausanne, Lausanne,

Switzerland

* raphael.nussbaume@vogelwarte.ch

Abstract

1. Quantifying nocturnal bird migration at high resolution is essential for (1)

understanding the phenology of migration and its drivers, (2) identifying critical

spatio-temporal protection zones for migratory birds, and (3) assessing the risk of

collision with man-made structures.

2. We propose a tailored geostatistical model to interpolate migration intensity

monitored by a network of weather radars. The model is applied to data collected

in autumn 2016 from 69 European weather radars. To cross-validate the model,

we compared our results with independent measurements of two bird radars.

3. Our model estimated bird densities at high resolution (0.2◦latitude-longitude,

15min) and assessed the associated uncertainty. Within the area covered by the

radar network, we estimated that around 120 million birds were simultaneously in

flight [10-90 quantiles: 107-134]. Local estimations can be easily visualized and

retrieved from a dedicated interactive website:

birdmigrationmap.vogelwarte.ch.

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4.

This proof-of-concept study demonstrates that a network of weather radar is able

to quantify bird migration at high resolution and accuracy. The model presented

has the ability to monitor population of migratory birds at scales ranging from

regional to continental in space and daily to yearly in time. Near-real-time

estimation should soon be possible with an update of the infrastructure and

processing software.

Keywords 1

Aeroecology, Bird migration, Geostatistical modelling, Interactive visualisation, Kriging,

2

Radar network, Spatio-temporal interpolation map, Weather radar. 3

Introduction 4

Every year, several billion birds undergo migratory journeys between their breeding and

5

non-breeding grounds (Dokter et al., 2018; Hahn, Bauer, & Liechti, 2009). These 6

migratory movements link ecosystems and biodiversity at a global scale (Bauer & Hoye,

7

2014), and their understanding and protection requires international efforts (Runge, 8

Martin, Possingham, Willis, & Fuller, 2014). Indeed, declines in many migratory bird 9

populations (Sanderson, Donald, Pain, Burfield, & van Bommel, 2006; Vickery et al., 10

2013) resulted from the rapid changes of their habitats, including the aerosphere (Diehl,

11

2013). Changes in aerial habitats are diverse, and their consequences still poorly 12

resolved. Nevertheless, climate change may alter global wind patterns and consequently

13

the wind assistance provided to migrants (La Sorte, Horton, Nilsson, & Dokter, 2019). 14

Likely more severe, the impact of direct anthropogenic changes include for instance light

15

pollution that reroute migrants (Van Doren et al., 2017), or buildings (Winger et al., 16

2019), wind energy production (Aschwanden et al., 2018), and aviation (van Gasteren et

17

al., 2019) that together cause billions of fatalities every year (Loss, Will, & Marra, 2015).

18

In the face of these threats and for setting up efficient management actions, we need

19

to quantify bird migration at various spatial and temporal scales. Fine scale monitoring

20

is crucial for understanding the phenology of migration and its drivers, identifying 21

critical spatio-temporal protection zones to enhance conservation actions, and assessing

22

2/20

collision risks with human-made structures and aviation to inform stakeholders. 23

However, the great majority of migratory landbirds fly at night (Winkler, 1999), 24

challenging the quantification of the sheer scale of bird migration. 25

Radar monitoring has the potential to quantify migratory movements of birds at the

26

continental scale (Drake & Bruderer, 2017). Initially limited to single dedicated 27

short-range measurements, the use of existing weather radar networks provide 28

continuous monitoring over large geographical areas such as Europe or North America 29

(Gauthreaux, Belser, & van Blaricom, 2003; Shamoun-Baranes et al., 2014), and led to

30

an upswing of radar aeroecology (Bauer et al., 2017; Dokter et al., 2018; Van Doren & 31

Horton, 2018). One important challenge in using networks of weather radars is the 32

interpolation of their signals in space and time. Recent studies (Dokter et al., 2018; Van

33

Doren & Horton, 2018) have used relatively simple interpolation methods as they 34

targeted patterns at coarse spatial and/or temporal scales. However, these methods are

35

insufficient if higher spatial or temporal resolution is wanted such as for the 36

fundamental and applied challenges outlined above. 37

To achieve high resolution interpolation of migration intensity derived from weather

38

radars ( 20km-15min), we propose a tailored geostatistical framework able to model the

39

spatio-temporal pattern of bird migration. Starting from time series of bird densities 40

measured by a radar network, our geostatistical model produces a continuous map of 41

bird densities over time and space. A major strength of this method is its ability to 42

provide the full range of uncertainty and thus, to evaluate the probability that bird 43

densities reaches a given threshold. In addition to the estimation map, the method also

44

produces simulation maps which are essential for several applications such as 45

quantification of the total number of birds. 46

As a proof of concept, we applied our geostatistical model to a three weeks dataset 47

from the European Network of weather radar (Huuskonen, Saltikoff, & Holleman, 2014)

48

and validated the results with independent dedicated bird radar data. In addition to 49

insights into the spatio-temporal scales of broad front migration, our approach provides

50

high resolution (0.2

◦

latitude and longitude, 15min) interactive maps of the densities of

51

migratory birds. 52

3/20

Materials and Methods 53

Weather radar dataset 54

Our dataset originates from measurements of 69 European weather radars, spread from

55

Finland to the Pyrenees (8 countries) and covering the period from 19 September to 10

56

October 2016 (Figure 1). It thus encompasses a large part of the Western-European 57

flyway during fall migration 2016. 58

50°N

60°N

0°E

10°E

20°E

30°E

69

Temporal resolution

143km

(+/- 45km)

Distance to closest radar

Number of radars

Scanning distance

510 15

3

7

59

25km

S

64

5

40km

25km

Figure 1.

(Left) Locations of weather radars of the ENRAM network, whose fall 2016-data were used in this study

(yellow dots), and their key characteristics (right panel). We used data from two dedicated bird radars – in Switzerland

and France - for validation (red dots).

Based on the reflectivity measurements of these weather radars, we used the bird 59

densities as calculated and stored on the repository of the European Network for the 60

Radar surveillance of Animal Movement (ENRAM) 61

(github.com/enram/data-repository)(see (Nilsson et al., 2019) for details on the 62

conversion procedure). We inspected the vertical profiles and manually cleaned the bird

63

densities data (see detailed procedure in Supporting Information S1). 64

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Since we targeted a 2D model, we vertically integrated the cleaned bird densities 65

from the radar elevation and up to 5000 m above sea level. Because we aimed at 66

quantifying nocturnal migration, we restricted our data to night time, between local 67

dusk and dawn (civil twilight, sun 6◦below horizon). Furthermore, as rain might 68

contaminate and distort the bird densities calculated from radar data, a mask for rain 69

was created when the total column of rain water exceeds a threshold of 1mm/h (ERA5

70

dataset from (Copernicus Climate Change Service (C3S), 2017). In the end, the 71

resulting dataset consisted of a time series of nocturnal bird densities [bird/km

2

] at each

72

radar site with a resolution of 5 to 15 min (Figure 2). 73

Interpolation approach 74

Bird densities are strongly correlated both spatially at continental (Figure 2a-d) to 75

regional scales (Figure 2c), and temporally at daily (Figure 2b-d) to sub-nightly scales 76

(Figure 2e-g). 77

100

20

30

40

50 (a)

(b)

(c)

(d)

Sep 27 Sep 28

2016

Bird densities [bird/km2]

0

10

20

0

50

100

50

10

Sep 22 Sep 25 Sep 28 Oct 01 Oct 04 Oct 07 Oct 10

2016

(e)

(f)

(g)

Date

0

100

200

0

100

200

Bird densities [bird/km2]

200

0

0

100

30

Figure 2.

Space-time variability of bird densities as measured by a radar network. (a) Average bird densities over the

whole study period (time series of radar with a coloured outer circle represented in the subsequent panels, respectively).

(b-d) Time series of bird densities measured at different locations (colour of the dots corresponds to the colour of the

outer circle in panel a). (e-g) Zoom on a two-days period.

These strong spatio-temporal correlations motivated the choice of using a 78

geostatistical framework to interpolate the punctual radar observations. In such 79

framework, bird densities are considered as a space-time random process that is fully 80

defined by its covariance matrix (e.g. Chil`es & Delfiner, 1999). To perform optimally, 81

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however, geostatistical interpolation requires bird densities to be stationary (i.e. mean, 82

variance and covariance) in both space and time (e.g. Chil`es & Delfiner, 1999) – an 83

assumption hardly ever satisfied for migratory events. Rather, there are two main and 84

obvious non-stationarities in our dataset: (1) migration is more intense in the south 85

than in the north of Europe (Figure 2a), and (2) migration is more intense in the 86

middle of the night than during twilight (Figure 2e-g). To account for these 87

non-stationarities, we develop a tailored geostatistical model that decomposes the 88

migration signal into four independent components. 89

Geostatistical model 90

The bird density Z(s, t) observed at location sand at time tis modelled by 91

Z(s, t)p=τ(s) + γ(s, t) + A(s, t) + R(s, t),(1)

where

p

is a power transformation,

τ

the continental trend,

c

is the curve describing the

92

nightly trend, Athe nightly amplitude, and Rthe residual term (Figure 3). A power 93

transformation is used on bird densities in order to transform the highly skewed 94

marginal distribution into a Gaussian distribution (Figure S3-1 in Supporting 95

Information S3). The trend and the curve are deterministic functions accounting for the

96

two non-stationarities, whereas the amplitude and the residuals are stationary random 97

processes modelling the spatio-temporal variability at nightly and sub-nightly scales 98

respectively. The four components of the model are detailed in the following 99

sub-sections. 100

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Sep 26, 12:00 Sep 27, 00:00 Sep 27, 12:00 Sep 28, 00:00 Sep 28, 12:00 Sep 29, 00:00 Sep 29, 12:00

2016

0

10

20

30

40

50

60

70

80

Bird densities [bird/km2]

Trend

Amplitude

Curve

Residual

-1 10

Normalized Night Time (NNT)

-1 10 -1 01

0

Date

Figure 3.

Illustration of the proposed mathematical model decomposition into trend, amplitude, curve and residual.

Note that the power transformation was not applied on this illustration.

Trend 101

The increasing bird densities southwards (Figure 2a) create a first non-stationary in the

102

dataset. Although this trend changes over the year, it can be considered constant over 103

the short study period. Therefore, we model the trend as a deterministic planar 104

function 105

τ(s= [slat, slon ]) = wlatslat +w0,(2)

where slat and slon are latitude and longitude of location s,wlat is the slope coefficient 106

in latitude and

w0

is the value of the trend at the origin. Because no longitudinal trend

107

is observed in the data (Figure 1a), only latitude is used to parametrize the trend 108

function (see Figure S3-2 in Supporting Information S3). It is worth noting that if 109

longer periods are considered, Eqn. 2 should be replaced by a more complex parametric

110

function in order to handle the emerging patterns of long term non-stationarity. 111

Curve 112

The second non-stationarity visible in the dataset is the nightly pattern (Figure 2e-g) 113

that results from the onset and sharp increase of migration activity after sunset, and its

114

slow decrease towards sunrise (e.g. Bruderer & Liechti, 1995). Similar to the trend, this

115

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pattern needs to be extracted from the original signal to avoid non-stationarity. This is

116

done using a curve template

c

for all nights and locations, defined as the polynomial of

117

degree 6 118

γ(s, t) =

i=6

X

i=0

aiNNT(s, t)i,(3)

where aiare the coefficients of the polynomial and NNT (Normalized Night Time) is 119

the standardized proxy of the progression of night defined as 120

NNT(s, t) = 2t−t↑(s, t)−t↓(s, t)

t↑(s, t)−t↓(s, t),(4)

where t↓(s, t) and t↑(s, t) are the times of civil dusk and dawn respectively. NNT is 121

defined such that the local sunrise or sunset occur at NNT =−1 and NNT = 1, 122

respectively. 123

Amplitude 124

After removing the non-stationarities with the trend and the curve, the amplitude A125

models the nocturnal bird densities at the daily scale as a stationary space-time random

126

process. Its value is therefore constant within a night at a given location but varies 127

between locations and between nights. It accounts for the correlation at the scale of 128

several hundred kilometers and several days (Figure 1). 129

Residual 130

The variation in bird densities not modeled by trend, curve and amplitude, is still 131

strongly correlated in space and time at the hourly scale (Figure 2e-g). 132

Model parameterization 133

The values of the model parameters are determined by fitting the model to the observed

134

bird densities. In the Supporting Information S3, the parametrisation procedure is 135

detailed and the significance of the resulting parameters of the model are discussed. 136

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Bird migration mapping 137

After parametrisation, the geostatistical model can be used to interpolate bird density 138

observations derived from weather radars to produce high resolution maps. The full 139

mathematical description of the procedure is detailed in Supporting Information S2 and

140

a brief outline is given below. 141

The estimation of the bird density at any unsampled location

Z

(

s0, t0

)

∗

is performed

142

by first estimating independently each component, and then recombining them 143

according to Eqn. 1. Estimating the deterministic components (i.e. trend and curve) is

144

straightforward since they can be computed by applying Eqn. 2 and 3 at the target 145

location and time s0, t0. Since the probabilistic components (amplitude and residual) 146

are modelled as random processes, the estimations of A(s0, t0)∗and R(s0, t0)∗are 147

performed by kriging (e.g. Chil`es & Delfiner, 1999; Goovaerts, 1997). An important 148

advantage of using kriging is that it expresses the estimation as a Gaussian distribution,

149

thus providing not only the “most likely value” (i.e. mean or expected value) but also a

150

measure of uncertainty with the variance of estimation. Tracking back the uncertainty 151

provided by kriging to the final estimation

Z

(

s0, t0

)

∗

is non-trivial but possible through

152

the use of a quantile function (see Supporting Information S2 for details). Consequently,

153

the estimation

Z

(

s0, t0

)

∗

is expressed as the median and its uncertainty range is defined

154

as the quantiles 10 and 90. A continuous space-time estimation (with uncertainty) map

155

is then computed by repeating the procedure for estimating a spatio-temporal point 156

s0, t0on a discrete set of points (i.e. grid). 157

In addition to the kriging estimation, we also provide simulation maps. Although 158

kriging is known to produce accurate point estimates, it leads to excessively smooth 159

interpolation maps (e.g. Goovaerts, 1997) and thus fails to reproduce the fine-scale 160

texture of the process at hand. Consequently, estimation should be complemented by 161

geostatistical simulation (e.g. Chil`es & Delfiner, 1999; Goovaerts, 1997) in applications

162

for which the space-time structure of the interpolation map matters (e.g. when 163

non-linear transformations are applied to the interpolated bird densities map, or when 164

aggregation in space or time is required). However, simulations come with a heavy 165

computational cost as a large ensemble of realisations is required to quantify the 166

uncertainty associated with the interpolation. 167

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In the case study presented in this paper, both estimation and simulations maps are

168

calculated on a spatio-temporal grid with a resolution of 0.2

◦

in latitude (43

◦

to 68

◦

) and

169

longitude (-5◦to 30◦) and 15 minutes in time, resulting in 127x176x2017 nodes. Over 170

this large data cube, the estimation and simulation are only computed at the nodes 171

located (1) over land, (2) within 200km of the nearest radar and (3) during nighttime (

172

NNT(t, s)<−1 or 1 < N N T (t, s)). 173

Validation 174

Cross validation 175

We tested the internal consistency of the model by cross-validation. It consists of 176

sequentially omitting the data of a single radar, then estimating bird densities at this 177

radar location with the model and finally, comparing the model-estimated value and 178

Z(s, t)∗observed data Z(s, t). The model is assessed by its ability to provide both the 179

smallest misfit errors, i.e. kZ(s, t)∗−Z(s, t)k, and uncertainty ranges matching the 180

magnitude of these errors. Because it is difficult to quantify both aspects for a 181

non-normalized variable, the normalized error of estimation is used on the power 182

transformation variable 183

Z(s, t)∗−Z(s, t)

σp

Z(s, t),(5)

where σp

Z(s, t) is the standard deviation of the estimation as defined in Eqn. S2-10 of 184

Supporting Information S2. 185

Comparison with dedicated bird radars 186

A second validation of our modelling framework (from data acquisition by weather 187

radars to geostatistical interpolation) is to compare model-predicted bird migration 188

intensities with the measurements of two dedicated bird radars (Swiss BirdRadar 189

Solution AG, swiss-birdradar.com) located in Herzeele, France (50◦53’05.6”N 190

2

◦

32’40.9”E) and Sempach, Switzerland (47

◦

07’41.0”N 8

◦

11’32.5”E). These bird radars

191

register single echoes transiting through the radar beam, allowing to compute migration

192

traffic rates (MTR) and average speed of birds aloft (Nilsson et al., 2018; Schmid et al.,

193

2019). 194

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Results 195

Validation 196

Cross validation 197

In our study, the normalized error of estimation over all radars has a near-Gaussian 198

distribution with mean 0.017 and variance of 0.60 (Figure S4-1 in Supporting 199

Information S4). The near-zero mean of the error distribution indicates that our model

200

provides non-biased estimations of bird densities, while the near-one standard deviation

201

supports that the model provides appropriate uncertainty estimates, albeit slightly 202

overconfident. The performance of the cross-validation shows radar-specific biases (i.e. 203

constant under- or over-predictions)(Figure S4-2 in Supporting Information S4). The 204

biases are not spatially correlated (Figure S4-3 in Supporting Information S4) and 205

therefore such biases do not originate from the geostatistical model itself (or of 206

country-specific data quality). Rather, these radar-specific biases probably come from 207

either the data, such as birds non-accounted for (e.g. flying below the radar), or error in

208

the cleaning procedure (e.g. ground scattering). In contrast, the variances of the 209

normalized error of estimation of each radar are close to 1 and thus, demonstrate the 210

accuracy of the estimated uncertainty range (Figure S4-2 and Figure S4-3 in Supporting

211

Information S4). 212

Comparison with dedicated bird radars 213

The daily migration patterns estimated by our model coincide generally well with the 214

observations derived from dedicated bird radars (Figure 4). First, the estimations of the

215

model correctly reproduce the night-to-night migration intensity, with the exception of a

216

few nights (27-30 September for Herzeele and 26/27 September for Sempach). Second, 217

the intra-night fluctuations are also properly reproduced (e.g. 4/5 October for both 218

radars). Over the whole validation period, the normalized estimation error has a mean

219

of 0.6 and a variance of 1.3 at Herzeele radar location (n=164), and a mean of -0.8 and

220

a variance of 1.3 at Sempach radar location (n=264). These normalized estimation 221

errors indicate a tendency of the model to slightly overestimate bird densities in 222

Herzeele and to underestimate it in Sempach. Finally, both variances were close to one,

223

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which shows that the model provides a reliable uncertainty range. Overall, the 224

root-mean-square error of the non-transformed variable (i.e. the actual bird densities) 225

was around 20 bird/km2for both radars, which demonstrates the good performance of 226

the model at these two test locations. 227

0

20

40

60

80

100

120

140

Bird densities [bird/km2]

Uncertainty range

Estimate Z*

Bird radar

Sep 19 Sep 22 Sep 25 Sep 28 Oct 01 Oct 04 Oct 07 Oct 10

Date 2016

0

50

100

150

200

(a)

(b)

Figure 4.

Comparison of the estimated bird densities (black line, 10-90 quantiles uncertainty range in grey) and the

bird densities (red dots) observed using dedicated bird radars at two locations in (a) Herzeele, France (50

◦

53’05.6”N

2

◦

32’40.9”E) and (b) Sempach, Switzerland (47

◦

07’41.0”N 8

◦

11’32.5”E). Note that because of the power transformation,

model uncertainties are larger when the migration intensity is high. It is therefore critical to account for the uncertainty

ranges (light gray) when comparing the interpolation results with the bird radars observations (red dots).

Application to bird migration mapping 228

The main outcome of our model is to estimate bird densities at any time and location 229

within the domain of interest. This is illustrated by the estimation of bird densities time

230

series at specific locations (e.g. Figure 4), and by the generation of bird densities maps

231

at different time steps (Figure 5). 232

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1 10 100 15050

Daily average bird density [bird/km2]

18:00 19:00 20:00 21:00 22:00 23:00

00:00 01:00 02:00 03:00 04:00 05:00

Rain

Figure 5.

Maps of bird densities estimation every hour of a single night (4/5 October). Civil sunset and sunrise limits

are visible on the first and last snapshots. The highest bird densities are in the corridor from Northern Germany to

southwestern France. Rain limits migration in Southern Poland, Czech Republic and Southern Germany. The sunrise and

sunset fronts are visible at 18:00 and 05:00 with lower densities close to the fronts. A rain cell above Poland blocked

migration on the Eastern part of the domain. In contrast, a clear pathway is visible from Northern Germany through to

Southwestern France.

While the estimation represents the most likely value of bird density at each node of

233

the grid (e.g. Figure 5), a simulation generate several realizations (i.e. equiprobable 234

outcomes of the migration process) that reproduce the space-time patterns of migration

235

(e.g. Figure 6). As a consequence, only realizations are able to reproduce number during

236

peak migration as noted when comparing the colorscale of Figure 5 and Figure 6. This

237

becomes important when assessing for instance the total number of birds aloft. 238

13/20

0

1

100

1000

Bird densities [bird/kmi

2]

Rain

Realization 1 Realization 2 Realization 3

Figure 6.

Snapshot of three different realizations showing peak migration (4 October 2016 21:30 UTC). The total

number of birds in the air for these realisations was 119, 126 and 120 million respectively. Comparing the similarity and

differences of bird densities patterns among the realisations illustrates the variability allowed by the stochastic model used.

The texture of these realisations is more coherent with the observations than the smooth estimation map in Figure 5.

For each of the 100 realisations, we computed the total number of birds flying over 239

the whole domain for each time step (Figure 7b). Within the time periods considered in

240

this study, the peak migration occurred in the night of 4/5 October with up to 120 241

million [10-90 quantiles: 107-134] birds flying simultaneously. Computing this on 242

sub-domains such as countries highlight the geographical differences in migration 243

intensity. For instance, on the same night, France had 44 [39-51] million birds aloft (89

244

bird/km2), 20 [15-25] million for Poland (65 bird/km2), and only 8 [7-10] million in 245

Finland (30 bird/km2) (Figure 7c). 246

0

50

100

Sep 19 Sep 22 Sep 25 Sep 28 Oct 01 Oct 04 Oct 07 Oct 10

Date 2016

0

10

20

30

40

50

Total number of bird aloft [millions]

Full domain France Poland Finland Uncertainty range

(a) (b)

(c)

Figure 7.

Averaged time series of the total number of birds in migration over the whole domain (black line), France (blue

line), Poland (yellow line) and Finland (red line) and their associated uncertainty ranges (10-90 quantiles, light grey).

14/20

The spatio-temporal dynamics of bird migration can be visualized with an animated

247

and interactive map (available online at birdmigrationmap.vogelwarte.ch with user 248

manual provided in Supporting Information S5), produced with an open-source script 249

(github.com/Rafnuss-PostDoc/BMM-web). In the web app, users can visualize the 250

estimated maps or a single simulation maps animated in time, as well as time series of 251

bird densities of any location on the map. In addition, it is also possible to compute the

252

number of birds over a custom area and download all of these data through a dedicated

253

API. 254

Discussion 255

The model developed here can estimate bird migration intensity and its uncertainty 256

range on a high-resolution space-time grid (0.2

◦

lat. lon. and 15 min.). The highest total

257

number of birds flying simultaneously over the study area is estimated to 120 million 258

[10-90 quantiles: 107-134], corresponding to an average density of 52 birds/km2. This 259

number illustrates the impressive magnitude of nocturnal bird migration, and resembles

260

values of peak migration estimated over the USA with 500 million birds and a similar 261

average density of 51 birds/km2(Van Doren & Horton, 2018). For more local results, 262

interactive maps of the resulting bird density are available on a website with a 263

dedicated interface that facilitates the visualisation and the export of the estimated bird

264

densities and their associated uncertainty (birdmigrationmap.vogelwarte.ch, see 265

Supporting Information S5 for a user manual). 266

Advantages and limitations 267

This paper presents the first spatio-temporal interpolation of nocturnal bird densities at

268

the continental scale that accounts for sub-daily fluctuations and provides uncertainty 269

ranges. In contrast to the methods based on covariates that are deemed more reliable 270

for extrapolation in space and time (Erni et al., 2002; Van Belle, Shamoun-Baranes, Van

271

Loon, & Bouten, 2007; Van Doren & Horton, 2018), our interpolation approach does not

272

require any external covariate per se (e.g. temperature, rain, or wind). Although local 273

features such as the approach of a rain front, the proximity to the ocean, or the 274

presence of mountains will affect bird migration, these were not explicitly accounted for

275

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in the current model. However, their influence on bird migration is partially captured 276

by the measurements of weather radars, so that, in turn, the interpolation implicitly 277

accounts for them. Yet, if such covariates are available, the model can easily be adapted

278

to incorporate information from these covariates through co-kriging (e.g. Chil`es & 279

Delfiner, 1999). However, adding these covariables to the interpolation is only 280

advantageous if the correlation between bird densities and these covariates is stronger 281

than the spatio-temporal correlation of the nearby radars. 282

In addition to quantifying bird migration at high resolution, we can also deduce the

283

spatio-temporal scales at which migration is happening from the covariance function of

284

the model (Figure S3-5 in Supporting Information S3). For instance, the amplitude of 285

bird migration correlates over distances up to 700 km and over periods of up to 5.5 days

286

(i.e. distance for which the auto-covariance has reached 10% of its baseline value, see 287

Supporting Information S3 for details). These decorrelation ranges of the amplitude 288

scale the spatio-temporal extent of broad front migration in the midst of the autumn 289

migration season and highlight the importance of international cooperation for data 290

acquisition and for spread of warning systems on peak migration events. 291

As a proof of concept, we used three weeks of bird densities data available on the 292

ENRAM data repository (see Data Accessibility). As more data from weather radars 293

become available, our analyses can be extended to year-round estimations of migration

294

intensity at the continental scale, in Europe and in North America. We also importantly

295

pre-processed the bird density data, i.e. restricted our model to nocturnal movements 296

and applied a strict manual data cleaning. This is because the bird density data 297

presently made available can be strongly contaminated with the presence of insects 298

during the day, and birds flying at low altitude are not reliably recorded by radars 299

because of ground clutter and the radar position in relation to its surrounding 300

topography. Once the quality of the bird density data has improved, our model can be

301

implemented in near-real-time and provide continuous information to the stakeholder, 302

public and private sector. 303

Although we think that the model introduced here can already be a valuable tool 304

(see below), we see several avenues for further development. For instance, in applications

305

where the distribution of flight altitudes is crucial, the model can be extended to 306

explicitly incorporate the vertical dimension. Furthermore, if fluxes of birds, i.e. 307

16/20

migration traffic rates, are sought after, a similar geostatistical approach can be used to

308

interpolate flight speeds and directions that are also derived from weather radar data. 309

Applications 310

Many applied problems rely on high-resolution estimates of bird densities and migration

311

intensities and the model developed here lays the groundwork for addressing these 312

challenges. For instance, such migration maps can identify migration hotspots, i.e. areas

313

through which many aerial migrants move, and thus, assist in prioritising conservation 314

efforts. Furthermore, mitigating collision risks of birds by turning off artificial lights of

315

tall buildings or shutting down wind energy installations requires information on when 316

and where migration intensity peaks. The probability distribution function of our model

317

can provide this as it estimates when and where migration intensity exceeds a given 318

threshold. Such information can be used in shut-down on demand protocols for wind 319

turbine operators, or trigger alarms to infrastructure managers. 320

Acknowledgements 321

This study contains modified Copernicus Climate Change Service Information 2019. Neither the European Commission 322

nor ECMWF is responsible for any use that may be made of the Copernicus Information or Data it contains. We 323

acknowledge the European Operational Program for Exchange of Weather Radar Information (EUMETNET/OPERA) 324

for providing access to European radar data, facilitated through a research-only license agreement between 325

EUMETNET/OPERA members and ENRAM (European Network for Radar surveillance of Animal Movements). 326

Mathieu Boos kindly provided the BirdScan data for Herzeele in France. We acknowledge the financial support from the

327

Globam project funded by BioDIVERSA, including the Swiss National Science Foundation (31BD30 184120), 328

Netherlands Organisation for Scientific Research (NWO E10008), Academy of Finland (aka 326315), BelSPO 329

BR/185/A1/GloBAM-BE. 330

Authors’ contributions 331

RN, LB, FL, BS conceived the study, RN, LB, GM designed the geostatistical model, RN developed and implement the

332

computational framework, RN, LB, BS performed the analyses and wrote a first draft of the manuscript, with substantial

333

contributions from all authors. 334

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Data Accessibility 335

•The Github page of the project (rafnuss-postdoc.github.io/BMM contains the MATLAB livescript for the 336

interpolation rafnuss-postdoc.github.io/BMM/2016/html/Density inference cross validation.html) and 337

the creation of the figures (rafnuss-postdoc.github.io/BMM/2016/html/paper figure). 338

•Raw weather radar data are available on the ENRAM repository (github.com/enram/data-repository). 339

•

The cleaned vertical time series profile are available on Zenodo (

doi.org/10.5281/zenodo.3243397

) (Nussbaumer,

340

Benoit, Mariethoz, et al., 2019) 341

•

The final interpolated maps are available on Zenodo (

doi.org/10.5281/zenodo.3243466

) (Nussbaumer, Benoit, &

342

Schmid, 2019). 343

•The code of the website (HTML, Js, NodeJs, Css) are available on the Github page 344

(github.com/rafnuss-postdoc/BMM-web)345

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Supporting Information 346

S1 Data pre-processing 347

Supporting Information S1 describes the full procedure applied to manually clean the raw time series of bird densities. 348

The raw dataset have been previously published in (Nilsson et al., 2019) and is available on the ENRAM data repository

349

(

github.com/enram/data-repository

). The steps detailed below are illustrated in Figure S1-1 for the radar located in

350

Zaventem, Belgium (50◦54’19”N, 4◦27’28”E). 351

1.

The data of 11 radars are discarded because their quality was deemed insufficient by visual inspection. The reasons

352

for this poor quality are various: S-band radar type, altitude cut, poor processing or large gaps. The same radars 353

were removed in (Nilsson et al., 2019). In addition, we also excluded radars of Bulgaria and Portugal (4 radars) from

354

this study because of their geographic isolation and the necessity of spatial coherence in the methodology presented.

355

2. If rain is present at any altitude bin, the full vertical profile was discarded (blue rectangle in Figure S1-1). A 356

dedicated MATLAB GUI was used to visualise the data and manually set bird densities to “not-a-number” in such

357

cases. 358

3.

Zones of high bird densities are sometimes incorrectly eliminated in the raw data (red rectangle in Figure S1-1). To

359

address this, (Nilsson et al., 2019) excluded problematic time or height ranges from the data. Here, in order to keep

360

as much data as possible, the data have been manually edited to replace erroneous data either with “not-a-number”,

361

or by cubic interpolation using the dedicated MATLAB GUI. 362

4.

Due to ground scattering, the lowest altitude layers are sometimes contaminated by errors, or excluded by the initial

363

automatic cleaning procedure. This is solved by copying the first layer without error into to the lowest ones. 364

5.

The vertical profiles are vertically integrated from the radar altitude (brown line in Figure S1-1c) and up to 5000 m

365

a.s.l. 366

6.

Finally, the data recorded during daytime are excluded. Daytime is defined at each radar by the civil dawn and dusk

367

(sun 6◦below horizon). 368

The resulting cleaned vertical-integrated time series of nocturnal bird densities are displayed in Figure S1-1d. 369

1/20

09/20 09/22 09/24 09/26 09/28 09/30 10/02 10/04 10/06 10/08

Date

0

1

2

3

4

5

-5

0

5

Bird Densities [bird/km3]

Altitude [km]

-60

-40

-20

0

20

Reflectivity

0

1

2

3

4

5

Bird Densities [bird/km2]

0

20

40

60

0

1

2

3

4

5

(a)

(b)

(c)

(d)

Rain Ground Scattering

Ground

Gap

Figure S1-1.

Example of the cleaning procedure from raw reflectivity to areal bird densities for the radar of Zaventem,

Belgium (50

◦

54’19”N, 4

◦

27’28”E). (a) raw reflectivity measurements; (b) Automatically cleaned vertical bird profiles; (c)

Manually cleaned vertical bird profiles; (d) Final bird densities (integrated over altitudes).

S2 Details on the geostatistical model 370

Supporting Information S2 expends the explanation given in the section Geostatistical model. In particular, it provides 371

the mathematical development for the kriging equations of the amplitude and residual as well as the reconstruction of the

372

bird densities estimation. 373

2/20

Standardization 374

For the convenience of the kriging equation, we introduce the standardized (i.e. normal transformed) variable

˜

A

(

s, t

) and

375

˜

R

(

s, t

) of the amplitude and residual respectively. Because the trend removed the average of the amplitude (i.e.

E

(

A

) = 0

376

), the standardized amplitude is 377

˜

A(s, t) = A(s, t)

σA

,(S2-1)

where σA=pvar (A) is the empirical standard deviation of A. The standardized residual is 378

˜

R(s, t) = R(s, t)

σR(s, t),(S2-2)

where the variance σR(s, t) is modelled by a polynomial function of the local NNT because of the strong correlation of 379

the variance of the residual with the NNT ( Figure S3-3 in Supporting Information S3), 380

σR(s, t) =

i=6

X

i=0

biNNT(s, t)i,(S2-3)

where biare the coefficients of the polynomial. 381

Covariance function 382

Both the amplitude and the residual are modelled as stationary processes which can be described with a covariance

function (also called auto-covariance). Let us denote the generic standardized random variable ˜

Xfor either the

standardized amplitude ˜

Aor the standardized residual ˜

R. The covariance C˜

Xis a positive definite function depending

only on the lag-distance (∆s,∆t). In our model, we use covariance functions of Gneiting type (Gneiting, 2002)

C˜

X(∆s,∆t) = cov ˜

X(s,t),˜

X (s+ ∆s,t + ∆t)

=C0+1

(∆t/rt)2δ+ 1 exp

−(k∆sk2/rs)2γ

(∆t/rt)2δ+ 1βγ

.

(S2-4)

In this model, rtand rsare the scale parameters (in space and time respectively). They control the decorrelation 383

distances and thus, the average extent and duration of the space-time patterns of ˜

X. 0 < δ,γ < 1 are regularity 384

parameters (in space and time respectively) and control the shape of the covariance function close to the origin. Values of

385

δand γclose to 0 lead to sharp variations at short lags, while values close to 1 lead to smooth variations of ˜

A. The 386

separability parameter βcontrols the space-time interactions. When β= 0 the space-time interactions vanish and the 387

covariance function becomes space-time separable. Finally, C0is the nugget, which accounts for the uncorrelated 388

3/20

variability of the process at hand. 389

Kriging 390

Both the standardized amplitude and residual can be estimated by kriging as explained below (Figure S2-1). Kriging 391

provides an estimated value of the random variable

˜

X

(

s0, t0

)

∗

at the target point (

s0, t0

) based on a linear combination of

392

observations at the n0closest space-time locations ˜

X(sα, tα)∗with 393

˜

X(s0, t0)∗=

α=n0

X

α=1

λα˜

X(sα, tα).(S2-5)

The kriging weights Λ= [λ1,· · · , λn0]Tare derived from the covariance function of the random process ˜

X. More 394

precisely, the kriging weights are the solution of the following linear system, commonly referred to as the kriging system,

395

Cα,αΛ=Cα,0,(S2-6)

with

Cα,α

the covariance matrix between observations and

Cα,0

the covariance matrix between the observations and the

396

target point. These covariances are computed using the fitted covariance function of Eqn. S2-4 397

Cα,0=C˜

X(sα−s0, tα−t0).(S2-7)

The kriging weights can be solved using Λ=C−1

α,αCα,0, and used in Eqn. S2-5 to compute the kriging estimate. 398

4/20

28-Sep

29-Sep

55

Time

30-Sep

20

50

Latitude 15

Longitude

10

45 5

0

-14

-10

-6

-2

Kriging Weight Value (log-scale)

Figure S2-1.

Illustration of the kriging weights computed for an estimation performed at the red dot location. Here we

illustrate only the neighbours whithin +/- 1 day and a spatial neighbourhood of 600 km.

In addition to the estimated value

˜

X(s0, t0)∗

, kriging also provides a measure of uncertainty with the variance of the

399

estimation, 400

var ˜

X (s0,t0)∗= C˜

X(0,0) −ΛtCα,0(S2-8)

Reconstruction of the transformed bird densities 401

The transformed variable Z(s0, t0)pis reconstructed by combining the deterministic parts (trend and curve) with the

kriging estimation of the amplitude and residual as in Eqn. 1. Because Aand Rare normally distributed, Zpis also

5/20

normally distributed and its mean µp

Zand variance σ2

Zpare sufficient to describe its distribution with

µZp=E(Z(s0, t0)p)

=E(t(s0) + A(s0, t0) + c(t0) + R(s0, t0))

=t(s0) + E(A(s0, t0)) + c(t0) + E(R(s0, t0))

=t(s0) + ˜

A(s0, t0)∗σA+c(t0) + ˜

R(s0, t0)∗σR(s0, t0)

(S2-9)

and as Aand Rare independent,

σ2

Zp= var (A(s0, t0) + R(s0, t0))

= var (A(s0, t0)) + var (R(s0, t0))

= (σ˜

A(s0, t0)σA)2+ (σ˜

R(s0, t0)σR(s0, t0))2.

(S2-10)

S2.1 Probability distribution function of bird densities 402

Because of the power-transform, the probability distribution function (pdf) of Z, denoted by fZ(z), is non-trivial. 403

However, the quantiles of this pdf can be derived analytically from the quantiles of the pdf of Zpas detailed hereafter. 404

We introduce the normally distributed variable X=Zpwith a pdf 405

fX(x) = 1

p2σ2

Zpπexp −(x−µZp)2

2σ2

Zp!,(S2-11)

where µZpand σ2

Zpare the mean and variance of Zpderived from Eqn. S2-9 and S2-10. 406

One possible way to compute the pdf of Zpconsists in computing the mean of several functions of this random 407

variable. For any given measurable function g,408

EgX1/p =

∞

Z

−∞

gx1/p fx(x) dx. (S2-12)

Using the change of variable z=x1/p , which leads to dx=pZp−1dz, Eqn. S2-12 becomes 409

E(g(Z)) =

∞

Z

−∞

g(z)pZp−1fX(Zp) dz. (S2-13)

6/20

This equation allows identifying the pdf of Zas 410

fZ(z) = pZp−1fX(x).(S2-14)

This last equation provides the analytical pdf of bird densities Z, as the pdf fX(x) = fZp(zp) is fully known 411

Zp∼ N µZp, σ2

Zp.412

Quantile function 413

The probability distribution function of

Z

is non-symmetric and skewed, and therefore cannot be conveniently described

414

with this expected value and variance. Instead, we use the quantile function

QZ(ρ;s0, t0)

, which returns the bird density

415

value zcorresponding to a given quantile ρ416

QZ(ρ;s0, t0) = z|Pr (Z(s0, t0)< z) = ρ. (S2-15)

The quantile function allows to describe Zbecause the quantile value ρis preserved through power transform. 417

Therefore, the quantile function of Zis computed with 418

QZ(ρ;s0, t0) = QZp(ρ;s0, t0)1/p =F−1

Zp(ρ)1/p ,(S2-16)

where FZp(Zp) is the cumulative distribution function of Zp(s0, t0). 419

S3 Model parametrisation 420

Supporting Information S3 presents the method of parametrisation and discusses the meaning of model parameters in 421

terms of bird migration. 422

Power transform 423

The value of power transformation pis inferred by maximizing the Kolmogorov-Smirnov criterion of the p-transformed 424

observation data Z(s, t)p. The Kolmogorov-Smirnov test (Massey, 1951) is testing the hypothesis that data Z(s, t)pare 425

normally distributed. The optimal power transformation parameter was found for p= 1/7.4 and the resulting Zp426

histogram is illustrated in Figure S3-1 together with the initial data Z.427

7/20

Figure S3-1.

Histogram of the raw bird densities data

Z

(top) and the power transformed bird densities

Zp

(bottom)

for the calibrated parameter p= 1/7.4.

The fitted distribution shows that bird densities is highly skewed: the lowest 10% are below 1 bird/km2while the 428

upper 10% are above 50 bird/km

2

with density up to 500 bird/km

2

. A power transformation on such skewed data creates

429

significant non-linear effects in the back-transformation. For instance, the symmetric uncertainty of an estimated value in

430

the transformed space (quantified by the variance of estimation) will become highly skewed in the original space. 431

Consequently, the uncertainty of the estimation of bird densities is highly dependent on the value of the power transform:

432

low densities estimations have a smaller uncertainty than high densities. This motivates the importance of providing the

433

full distribution of the estimation. Indeed, the traditional central value (mean of 19 bird/km

2

and median of 8 bird/km

2

)

434

would be unable to capture the distribution adequately. Such effects also have consequences from an 435

ecological/conservation point of view. Indeed, efficient protection of birds along the migration route (from artificial light

436

or wind turbines) need to pay particular attention to the peak densities, where the majority of birds are moving in a few

437

nights. These peaks can only be successfully reproduced by taking care of the high tail of the distribution. This is done

438

here by using a full distribution for the estimation. 439

Trend and curve 440

The parameters of the deterministic components of the model (i.e. trend and curve) are calibrated based on the 441

transformed data measured at the radar locations. This step involves the calibration of 3 parameters for the trend 442

(wlat, wlon , w0), 6 for the curve (ai) and also the values of the amplitude for each radar and for each night (i.e. 443

nradar ·nday values). The calibration is performed by minimizing the misfit function between the modeled and the 444

observed data. In practice, a local search algorithm is used (fminsearch function of MATLAB which uses a simplex 445

8/20

algorithm). This local search algorithm requires initial values for each parameter, which are computed sequentially: (1) 446

the initial trend is fitted to the average of the transformed bird densities for each radar, (2) the amplitudes are computed

447

from the de-trended data, and (3) the parameters of the curve are derived by fitting a polynomial on the data corrected

448

from the trend and amplitude effects. After convergence of the algorithm, the resulting misfit value becomes the value of

449

the residual. The resulting planar trend is shown in Figure S3-2a together with the average transformed bird densities of

450

each radar. The trend displays a strong North-South gradient, which can be explained by the larger migration activity in

451

southern Europe during the study period. A 2-dimensional planar trend was initially tested in order to accommodate the

452

northeast-southwest flyway. However, this more complex model did not significantly improved the fit to data, and has 453

therefore been discarded. The de-trended values illustrated in Figure S3-2b are more stationary with the exception of 454

Finland and Sweden. (Nilsson et al., 2019) also noted this difference between both countries, but excluded the fact that

455

this difference is due to errors in the data since the southern Swedish radar shows consistent amounts of migratory 456

movements with a neighbouring German site. Figure S3-2b highlights the central European continental flyway as 457

illustrated by the arrow. 458

Transformed bird densities

-0.3

-0.2

-0.1

0

0.1

0.2

1

1.2

1.4

1.6

Transformed bird densities

Figure S3-2. (left) Fitted trend with corresponding observation at radar location and (right) detrended data.

Figure S3-3 displays the fitted curve (black line) together with the calibration data. The curve reveals that the 459

migration is mainly concentrated between 10-90% of the nighttime with larger densities of birds in the first half of the 460

night. A slight asymmetry with steeper rise at the beginning of the night and smoother transition with the day is also 461

visible. The larger variance of the data around the calibrated curve at the beginning and end of night is due to the 462

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power-transformation of the raw data and accounted for in the model. However, the large variance of the data used to 463

adjust the curve model shows a significant intra-night variability in bird migration. This highlights the importance of 464

modelling the intra-night fluctuations by the residual term and stresses the limitation of using nightly averages or single

465

point observations (e.g. 3hr after sunset) if high precision estimates are required. 466

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

Normalized Night Time (NNT)

-1.2

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

Transformed bird densities

Figure S3-3.

Individual observations (black dots) and adjusted model (black line) of the nightly curve. Shaded grey

areas denote 1-, 2- and 3- sigma uncertainty ranges.

As no clear spatial patterns appear in the curve parameters, a single curve model is used for the entire study domain.

467

The suitability of this unique curve model is validated by the spatially-uncorrelated mean and variance of the residual 468

signal displayed in Figure S3-4. 469

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-0.2

-0.1

0

0.1

0.2

0.5

1

1.5

(a) (b)

Figure S3-4. (a) Mean and (b) standard deviation of residual value for each radars.

Amplitude and residual 470

The parameters of the space-time covariance function (n, rt, rs, δ, γ, β) of the amplitude and residual are inferred from 471

empirical covariances derived for several lag-distances and lag-times on an irregular grid. Then, the parameters of the 472

Gneiting covariance function are inferred by minimizing the root mean square error between empirical and modelled 473

covariances. Both covariance functions of the amplitude and residual are best fitted with a separable model (β= 0), 474

meaning that they can be fully described by the product of a spatial covariance function (Figure S3-5a and c) and a 475

temporal covariance function (Figure S3-5 b and d). 476

Covariance function of the amplitude and residual 477

The calibrated covariance functions provide information about the degree of spatial and temporal correlation of the bird

478

migration process. The spatial covariance of the amplitude (Figure S3-5a) shows that the nocturnal bird densities are 479

well-correlated for locations separated by less than 500 km, and completely uncorrelated for more than 1500 km. The 480

temporal covariance has an asymptotic behavior and never decreases under 0.2 (Figure S3-5b). This non-zero sill can be

481

due to either a remaining temporal non-stationarity in the dataset, or systematic errors in radar observations (caused by

482

e.g. different types of technology or local topography affecting migration). Note that since the covariance is evaluated 483

only on a discrete 1-day lag-distance, the shape of the covariance between 0 and 1 is artificially created to fit the Gneiting

484

function. Overall, the temporal correlation of the amplitude is weak with only 40% for the covariance for lag-1. It is 485

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Table 1. Calibrated parameters

Power Transformation p= 0.135

Trend w0= 2.62 , wlat =−0.024

Covariance of amplitude nugget/sill = 0%, β= 0, rt= 0.39, rs= 174, δ= 0.18,

γ= 0.43

Curve a= [−0.720.120.76 −0.05 −0.29 −0.070.05]

Curve variance b= [−0.010.030.00 −0.010.000.00]

Covariance of residual nugget/sill = 7.7%, β= 0, rt= 0.048, rs= 206, δ= 1,

γ= 0.47

important to recall that since the weather radars are relatively well-spread (Figure 1b), the spatial covariance of both the

486

amplitude and residual is poorly constrained for lag-distances below 100 km, and consequently the importance of the 487

nugget (Eqn. S2-4) is unknown. The temporal correlation of the residual is very high for short lags (

<

2 hr) and indicates

488

consistent measurements of each weather radars. The small covariance value for larger lag-distances demonstrates that 489

the curve account for most of the stationary component at this scale. 490

0 500 1000 1500 2000

0

0.5

1

0246810

0 200 400 600 800 1000

Distance [km]

0

1

Covariance

0 0.1 0.2 0.3 0.4

Time [Days]

(b)(a)

(c) (d)

Residual Amplitude

0.5

Figure S3-5. Illustration of the calibrated covariance function of (a-b) amplitude and (c-d) residual.

The table below summarizes the fitted parameters. 491

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S4 Cross-validation 492

Supporting Information S4 extends the results of the Cross-validation section. First of all, Figure S4-1 displays the 493

histogram of the normalized errors of kriging (Eqn. 5) when all data across all radars are combined. The mean of the 494

distribution is close to zero which indicates that the estimation is unbiased (i.e. in average, the estimation is neither 495

underestimating (mean below 1) nor overestimating (mean above 1)). However, its variance is below 1, which indicates a

496

slight overestimation of the uncertainty range (i.e. in average, the uncertainty ranges are too wide). 497

-4 -3 -2 -1 0 1 2 3 4

0

0.1

0.2

0.3

0.4

0.5

0.6

Normalized error of kriging with mean: -0.017 and variance: 0.61

Figure S4-1.

Histogram of the normalized error of kriging for all radars combined. The red curve is the standard normal

distribution which should be matched by the histogram.

Next, the normalized kriging error is assessed for each radar (Figure S4-2). The resulting distributions indicate that 498

the goodness of the estimation is different for each radar. In Figure S4-3, their means and standard deviations do not 499

reveal any spatial pattern, thus suggesting no spatial biases. 500

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bejab

bewid

bezav

czbrd

czska

deboo

dedrs

deeis

deess

defbg

defld

dehnr

deisn

demem

deneu

denhb

deoft

depro

deros

detur

deumd

fianj

fiika

fikes

fikor

fikuo

filuo

fipet

fiuta

fivan

fivim

frabb

frave

frbla

frbor

frbou

frcae

frche

frgre

frlep

frmcl

frmom

frmtc

frniz

frpla

frtou

frtra

frtre

frtro

nldbl

nldhl

plbrz

plgda

plleg

plpoz

plram

plrze

plswi

seang

searl

sease

sehud

sekir

sekkr

selek

selul

seovi

sevar

sevil

-4

-3

-2

-1

0

1

2

3

4

Normalized error of kriging

Figure S4-2.

Boxplot of the normalized kriging error for each radar. A negative (positive) value indicates an

underestimation (overestimation) of the method. The cross-validation for the Czech (czbrd, czska) and Swedish radars

(se***) shows a constant underestimation (except for selul). Overall, the goodness of the estimation is variable and

radar-dependent.

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0.5

-1

-1.5

0.5

0

1

1.5

1

1.5

0.5

Mean

Variance

Figure S4-3.

Mapping of the mean and variance of the normalized error of kriging for each radar. The reproduction of

the variance is illustrated by a black circle, for which a perfect variance would match the colour circle and a smaller circle

indicates an under-confidence (uncertainty range too large).

The cross-validation is further illustrated in Figure S4-4 for a specific radar located in Boostedt, Germany 501

(54

◦

00’16”N, 10

◦

02’49”E) indicated with gold circle in Figure S4-3. For this radar, the general pattern of the signal is well

502

estimated for both the nightly amplitude and the intra-night variation. Bird densities are underestimated during the peak

503

migration occurring at 4th and 5th of October, is but the estimated value remains within the uncertainty bounds. 504

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25-Sep 02-Oct 09-Oct

Date

0

50

100

150

200

250

Bird densities [bird/km

2]

Uncertainty range

Estimate Z*

Weather radar data

Figure S4-4.

Comparison of bird densities estimated with the model in a cross-validation setup and observed by the

weather radar for the radar located in Boostedt, Germany (54

◦

00’16”N, 10

◦

02’49”E). The uncertainty range is defined as

the 10 and 90 quantiles.

S5 Manual for website interface 505

The following Supporting Information describes the web interface developed for visualization and querying of the 506

interpolated data. The website is available at birdmigrationmap.vogelwarte.ch and the code at 507

github.com/Rafnuss-PostDoc/BMM-web. Figure S5-1 displays the web interface along with the possible interactions, 508

which are further detailed below. 509

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Figure S5-1. Website interface with identification key for the interactive components of each block

Block 1: interactive map 510

The main block of the website is a map with a standard interactive visualization allowing for zoom and pan. On top of 511

this map, three layers can be displayed: 512

•

Layer 1 corresponds to bird densities displayed in a log-color scale. This layer can display either the estimation map,

513

or a single simulation map by using the drop-down menu (1a). 514

•

Layer 2 corresponds to the rain (rainy areas are in light blue), which can be hidden/displayed with a checkbox (1b)

515

•Layer 3 corresponds to the bird flight speed and direction, displayed by black arrows. The checkbox allows to 516

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display/hide this layer (1c). The last item on the top-right menu is the link menu (1d). 517

Block 2: time series 518

The second block (hidden by default on the website) shows three time series, each in a different tab (2a): 519

•Densities profile shows the bird densities [bird/km2] at a specific location. 520

•Sum profile shows the total number of bird [bird] over an area. 521

•MRT profile shows the mean traffic rate (MTR) [bird/km/hr] perpendicular to a transect. 522

A dotted vertical line (2d) appears on each time series to show the current time frame displayed in the map. Basic 523

interactive tools for time series include zooming on a specific time period (day, week or all period) (2b) and general zoom

524

and auto-scale (2e). Each time series can be hidden and displayed by clicking on its legend (2c). The main feature of this

525

block is the ability to visualise bird densities time series for any location chosen on the map. For the densities profile tab,

526

the button with a marker icon (2f) lets you plot a marker on the map, and displays the bird densities profile with 527

uncertainty (quantile 10 and 90) on the time series corresponding to this location. You can plot several markers to 528

compare the different locations (Figure S5-2). Similarly, for the sum profile, the button with a polygon icon (2f) lets you

529

draw any polygon and returns the time series of the total number of birds flying over this area. For the MTR tab, the 530

flux of birds is computed on a segment (line of two points) by multiplying along the segment the bird densities with the

531

local flight speed perpendicular to that segment. 532

Block 3: time control 533

The third block shows the time progression of the animated map with a draggable slider (3d). You can control the time

534

with the buttons play/pause (3b), previous (3a) and next frame (3c). The speed of animation can be changed with a 535

slider (3e). 536

API 537

An API based on mangodb and NodeJS is available to download any of the time series described in Block 2. Instructions

538

can be found at github.com/Rafnuss-PostDoc/BMM-web#how-to-use-the-api 539

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Examples 540

Figure S5-2.

Print-screen of the web interface developed to visualize the dataset. The map shows the estimated bird

densities for the 23rd of September 2016 at 21:30 with the rain mask appearing in light blue on top. The domain extent is

illustrated by a black box. The time series in the bottom shows the bird densities with quantile 10 and 90 at the two

locations symbolized by the markers with corresponding color on the map. The button with a marker symbol on the right

side of the time series allows to query any location on the map, and to display the corresponding time series.

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Figure S5-3.

Print-screen of the web interface with the simulation map for the 3rd of October at 23:00. The bottom

panel shows the time series of the total number of birds corresponding to the polygon drawn over the map according to

their colour. The button with the polygon symbol on the right side of the time series allows to query the total number of

birds flying any polygon drawn on the map.

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